Answer
See below:
Work Step by Step
(a)
Cost function is sum of fixed cost and cost of number of desk producing,
\[C\left( x \right)=60000+200x\]
(b)
Revenue function is the amount of number of desk sold,
\[R\left( x \right)=450x\]
(c)
The break-even point occurs when the functions, C and R intersect.
C and R form a system of linear equation
\[\left\{ \begin{align}
& y=60000+200x \\
& y=450x \\
\end{align} \right.\]
Substitute \[y=450x\] in \[y=60000+200x\]
\[\begin{align}
& 450x=60000+200x \\
& 250x=60000 \\
& x=240
\end{align}\]
Back substitute the value of y,
\[\begin{align}
& y=450x \\
& =450\left( 240 \right) \\
& =108000
\end{align}\]
The break-even point is \[\left( 240,108000 \right)\]
The break-even point specifies that, company has to produce more than 240 desks to make a profit, if fails, company is in loss. If it produces 240 desks, 108000 is the equal money in producing and selling the desks.
